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The purpose of this short report is to introduce a branching random walk in random environment on $Z^d$ where particles perform independent simple random walks and branch according to a law that is obtained by fixing branching numbers at each point of $Z^d$. These numbers represent a realization of an integer-valued random field on $Z^d$ with the value at each point being independent of those at o
In this paper we study random walks with branching. We introduce the notion of recurrence and transience for these processes and provide criteria for them. For Lamperti problem and many-dimensional random walk with branching we nd the critical (for transience vs. recurrence) speed of decaying of the average number of o -springs at a point with respect to the distance from it to the origin.
We investigate the ecological and evolutionary variables that best explain spatial diversity patterns of anuran amphibians in three of South America's most diverse and geographically widespread biomes: the Cerrado, Amazonia, and Atlantic Rainforest. We used Conditional Autoregressive Models to assess the potential influence of present-day climate (temperature and precipitation), historical climate
Vertex-reinforced random walk (VRRW), defined by Pemantle, is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on almost all of them, VRRW visits only finitely many vertices with a positive probability. We conjecture that on all graphs of bounded degree, this happens with probabili
A stochastic process called vertex-reinforced random walk (VRRW) is defined in Pemantle [Ann. Probab. 16 1229-1241]. We consider this process in the case where the underlying graph is an infinite chain (i.e., the one-dimensional integer lattice). We show that the range is almost surely finite, that at least five points are visited infinitely often almost surely and that with positive probability t
We study the continuous time integer valued process Xt, t ≥ 0, which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent at that neighbor. We show that the proportion of the time before t which this process spends at integers j converges to positive random variables Vj, which sum to one, and whose joint distribution is explicitly descr
Since Jean-Paul Sartre’s conception of le regard des autres in 1943, ‘the gaze’ has taken on many manifestations. The male gaze, the white gaze, the imperial gaze, the postcolonial gaze. All imply a power to objectify, to define an Other, usually from a distance or even, as Donna Haraway described objectivity, from 'nowhere.' Museums have always held the power to define Others while claiming objec
Since Jean-Paul Sartre’s conception of le regard des autres in 1943, ‘the gaze’ has taken on many manifestations. The male gaze, the white gaze, the imperial gaze, the postcolonial gaze. All imply a power to objectify, to define an Other, usually from a distance or even, as Donna Haraway described objectivity, from 'nowhere.' Museums have always held the power to define Others while claiming objec
Rivers play a fundamental role in shaping the Earth’s surface and sustaining ecosystems. Accurate modeling and simulation of stream power are essential for understanding fluvial processes. As a measure of the energy exerted by overland flow, stream power possesses both magnitude and directional attributes. However, conventional simulation approaches based on scalar operations often neglect the dir
We consider the OK Corral model formulated by Williams and McIlroy and later studied by Kingman. In this paper we refine some of Kingman's results, by showing the connection between this model and Friedman's urn, and using Rubin's construction to decouple the urn. Also we obtain the exact expression for the probability of survival of exactly S gunmen given an initially fair configuration.
What is the effect of punching holes at random in an infinite tensed membrane? When will the membrane still support tension? This problem was introduced by Connelly in connection with applications of rigidity theory to natural sciences. The answer clearly depends on the shapes and the distribution of the holes. We briefly outline a mathematical theory of tension based on graph rigidity theory and
Many animals, such as birds and bats, are capable of migrating over vast distances to specific destinations. Remarkably, even insects such as the North American Monarch butterfly and the Australian Bogong moth undertake similarly long-distance migrations to specific sites. Here, we provide an overview of our current understanding of the migration of these insects and outline the sensory cues and n
We perform a validation analysis on the multipolar model of opinion dynamics. A general methodology for using the model on datasets of two correlated variables is proposed and tested using data on the relationship between COVID-19 vaccination rates and political participation in Sweden. The model is shown to successfully capture the opinion segregation demonstrated by the data and spatial correlat
Background Obstructive sleep apnea (OSA) is associated with cardiovascular morbidity; however, it remains unclear whether the apnea–hypopnea index (AHI) or the severity of nocturnal hypoxemia, in terms of oxygen desaturation index (ODI), is more relevant for the development of heart failure (HF). Methods We included 3590 participants from the Sleep Apnea Patients in Skaraborg Study (mean age 54.6
We consider a Markov chain on a countable state space, on which is placed a random field of traps, and ask whether the chain gets trapped almost surely. We show that the quenched problem (when the traps are fixed) is equivalent to the annealed problem (when the traps are updated each unit of time) and give a criterion for almost sure trapping versus positive probability of nontrapping. The hypothe
We consider a nearest-neighbor stochastic process on a rooted tree G which goes toward the root with probability 1 − ε when it visits a vertex for the first time. At all other times it behaves like a simple random walk on G. We show that for all ε ≥ 0 this process is transient. Also we consider a generalization of this process and establish its transience in some cases.
We consider some generalizations of the germ-grain growing model studied by Daley, Mallows and Shepp (2000). In this model, a realization of a Poisson process on a line with points Xi is fixed. At time zero, simultaneously at each Xi, a circle (grain) starts growing at the same speed. It grows until it touches another grain, and then it stops. The question is whether the point zero is eventually c
We study the continuous time process on the vertices of the b-ary tree which jumps to each nearest neighbor vertex at the rate of the time already spent at that vertex times δ, plus 1, where δ is a positive constant. We show that for fixed b > 1, if δ is large enough the process is transient, and if δ is close enough to zero it is recurrent. Related results for some other graphs and trees are also
Cognitive scientists Spelke and Kintzler (2007) and Carey (2009) identify objects, actions, space and numbers as “core domains of knowledge” that are essential for conceptualizing the world. Gärdenfors (2019, 2020) argues that objects, actions and space are characterized by invariances in sensory signals. In this paper, we extend the analysis of invariances to the domain of numbers (understood as
